RE: Strength +/-45 vs 0/90

You have to transform the stiffness, not just the stress, like the attached. You will see the order of the terms for stiffness (4th order) is different that for just a stress (or strain) transformation (2nd order). By the way, strength is very different from stiffness.

RE: Strength +/-45 vs 0/90

Do you mean aside from the 0/90 orientation putting fibers in direct tension, where they are very stiff while the 45 orientation puts them in bending, where they are not stiff? Stiffness is driven by the outer fibers so the layer contributionss can't be simply added.

RE: Strength +/-45 vs 0/90

A composite laminate is not just a material, it is a structure and you have to follow the load path to understand its behavior. In +/-45 laminates the load does not simply go down the length of the fiber from one end to the other. First, at a 45 degree angle there will be 1.42 times more fiber length in getting from one end to the other. This means more stretch, less stiffness. Second, load has to transfer from layer to layer by shear loading of the resin matrix. Resin is orders of magnitude less stiff than carbon fiber. Third, under load the fibers will scissor and change orientation, again only resisted by resin stiffness.

In a 0/90 laminate the resin carries very little load and its function is primarily to keep the fibers from buckling.

RE: Strength +/-45 vs 0/90

- In the post title, you say strength. But for your question, you ask about stiffness. Perhaps you made a mistake in your title, but I wanted to be clear about this distinction.

- The axial and bending stiffness of the laminate is simply (and directly) determined via classical laminate theory (CLT); there are no complex physical phenomena going on. For each ply, you must determine the stiffness properties in the transformed system (which is the matrix above). Any composite book will show you how this is done. The axial stiffness of the laminate is represented by the summation of each ply's stiffness contribution. The bending stiffness is represented by the stiffness of each ply and its area moment of inertia contribution (position within the ply). These are known as the [A] and [D] matrices (and [a], [d] matrices). The first point is that you can not just use the "square root of 2" approach since the order of the terms for a stiffness transformation is not 2nd order (it is 4th order). Again, look you will need to first understand the posted equation and how it is developed (for the primary contribution for the 45 ply, it is 0.707^4 = 0.25, not 0.707^2 = 0.5). The second point is that for bending you must also consider the inertia effect and the fact that neutral axis for the 0/90 is not at the midsurface (its closer to the center of the 0 ply) while the neutral axis for the 45/-45 is at the midsurface (so there is a bit more going on).

P.S. Because this is a stiffness problem (and not a strength problem), you do not need to consider any complex effects (interlaminar effects, etc.). You simply treat each ply as a rotated homogeneous orthotropic material (note that an off-axis ply has shear-extension coupling); fortunately, this has been shown to correlate well to experimental data. If you are discussing strength, then all bets are off; there is a more complex interaction between the plies that needs to be accounted for. But that is an entirely different topic; there have been several threads dedicated to that in the past.